Goitom was born in Solna, Stockholm, and raised in nearby Husby. His parents were born in Eritrea.
Goitom moved to Italy in 2004 to join Udinese Calcio, rarely being an option during his short stay. However, in his sole Serie A appearance, on 19 February 2005, he only needed seven minutes as a late substitute to score the 90th minute 1–1 equalizer against Inter Milan.
Subsequently, Goitom served a two-year loan in the Spanish second division with Ciudad de Murcia. He netted 15 league goals during his second season.
In 2007, Goitom was released by Udinese and signed a four-year deal with neighbouring Real Murcia, for a reported €3 million. The president of UD Almería, Alfonso García, however, announced the club would take matters to court: as he appeared before the media during the presentation of Aitor López Rekarte, showed journalists papers which proved an agreement had already been reached between Almería and Udinese.
With Murcia, Goitom only scored twice during the entire campaign, which saw the team eventually relegated from La Liga as last. In July 2008 he was loaned for one season to fellow league side Real Valladolid, which had an option to buy at the campaign's closure.
Established as first-choice, Goitom netted twice as Valladolid beat Recreativo de Huelva 3–2 away on 8 March 2009, but was also sent off during the match (as teammate Álvaro Rubio). He finished the season as team top scorer, at ten.
In late July 2009, Goitom was released by Murcia and joined fellow league side Almería, replacing Sevilla FC-bound Álvaro Negredo. His 2009–10 season output consisted of one goal, in a 1–1 home draw against CD Tenerife; also, even though he was the only pure striker in the squad, he was never an undisputed starter, but the Andalusians retained their top division status in the end.
On 19 January 2011, Goitom scored one of Almería's most important goals, netting a penalty kick in a 3–2 win at Deportivo de La Coruña (4–2 on aggregate), with the club reaching the semi-finals of the Copa del Rey for the first time ever (he added one more in the competition, against Real Sociedad). However, he again only netted once in the league, in a 2–2 home draw against Atlético Madrid, and the club returned to the second division after four years; in mid-August 2012, he terminated his contract.
On 16 August 2012, Goitom signed with his hometown club AIK Fotboll in the Allsvenskan. In November 2015, it was announced he would be released when his contract ended on 31 December.
On 22 March 2016, after being without a club for almost three months, Goitom agreed a short-term deal at Getafe CF. He made his debut about a week later, coming on as a second half-substitute in a 0–2 away loss against Rayo Vallecano.
Goitom only totalled 125 minutes of action during his spell, and his team suffered top flight relegation.
On 10 August 2016, Goitom joined San Jose Earthquakes on a free transfer. He made his Major League Soccer debut nine days later, coming from the bench in a 1–2 loss to Houston Dynamo at the Avaya Stadium.
At the end of the season, where he only started in two of his appearances, the club announced that they would not be exercising their option to extended Goitom's contract.
On 3 March 2017, it was announced that Goitom had signed a two-year contract with his former club AIK, thus returning to his birth country and its top flight.
Goitom was a regular starter for the Swedish under-21 team during 2006, and played for the nation during qualification for the 2006 and 2007 UEFA European Championships. He was on the verge of breaking into the full squad for the 2006 FIFA World Cup squad in Germany, but did not make the final cut.
In September 2015, at age of 30, Goitom made an official request to FIFA for permission to play for Eritrea. On 10 October he gained his first cap, in a 0–2 home loss to Botswana for the 2018 FIFA World Cup qualifiers; he scored in the return leg, to a final 1–5 defeat on aggregate.As of match played 13 May 2017
As of match played 13 October 2015
Scores and results list Eritrea's goal tally first.